derivative y=2xarccos(x)-2sqrt(1-x^2)

Lösung

ableitung von

y = 2 x arccos (x) - 2 1 - x^{2}

2 arccos (x)

Schritte zur Lösung

\frac{d}{d x} (2 x arccos (x) - 2 1 - x^{2})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (2 x arccos (x)) - \frac{d}{d x} (2 1 - x^{2})

\frac{d}{d x} (2 x arccos (x)) = 2 (arccos (x) - \frac{x}{1 - x ^{2}})

\frac{d}{d x} (2 1 - x^{2}) = - \frac{2 x}{1 - x ^{2}}

= 2 (arccos (x) - \frac{x}{1 - x ^{2}}) - (- \frac{2 x}{1 - x ^{2}})

Vereinfache

2 (arccos (x) - \frac{x}{1 - x ^{2}}) - (- \frac{2 x}{1 - x ^{2}}) : 2 arccos (x)

= 2 arccos (x)

n = 0 \sum \infty \frac{( n )}{n + 1}

\frac{y}{x ^{2}} \frac{d y}{d x} + e^{2 x^{3} + y^{2}} = 0

x \to \infty lim (\frac{4}{x} - 12)

\frac{\partial}{\partial y} (3 x + 2 y sin (x))

x \to 20 lim (sin (70 - x))